public static Portfolio CalculateLinear(double[,] equity, double reliability, double maximumLoss, double minimumCoefficientValue)
{
CalculateLinearValidation(reliability, maximumLoss);
double[,] deltaEquity = NumericalMethods.CalculateAbsoluteVariation(equity);
double[,] sigma = Statistics.CalculateCovarianceMatrix(deltaEquity);
double factor = NumericalMethods.Sqrt(sigma.Maximum());
if (factor <= 0)
{
string st = string.Format("Runtime error: invalid factor = {0}", factor);
throw new InvalidOperationException(st);
}
NumericalMethods.Multiply(deltaEquity, 1 / factor);
double[] profit = Statistics.CalculateAverage(deltaEquity);
sigma = Statistics.CalculateCovarianceMatrix(deltaEquity);
MathArgs args = new MathArgs();
args.Add("$profit", profit);
args.Add("$reliability", reliability);
args.Add("$covariance", sigma);
args.Add("$loss", maximumLoss / factor);
args.Add("$coefficient", minimumCoefficientValue);
Dictionary <string, object> output = MathematicaKernel.Execute(s_portfolioDiscrete, args);
Portfolio result = new Portfolio();
result.Profit = (double)output["profit"] * factor;
result.When = (double)output["when"];
result.Coefficients = (double[])output["result"];
return(result);
}
public static Interval CalculateConfidenceInterval(double[] data, double confidenceLevel)
{
if ((confidenceLevel <= 0) || (confidenceLevel >= 1))
{
string st = string.Format("Confidence level = {0}, but must be more than 0 and less than 1", confidenceLevel);
throw new ArgumentException(st);
}
double average;
double s2 = CalculateSampleVarianceAndAverage(data, out average);
MathArgs args = new MathArgs();
args.Add("$level", confidenceLevel);
args.Add("$freedom", data.Length - 1);
MathResult answer = s_confidenceIntervalCache.LookFor(args);
if (null == answer)
{
answer = MathematicaKernel.Execute(s_confidenceInterval, args);
s_confidenceIntervalCache.Add(args, answer);
}
double deviation = (double)answer["deviation"];
double k = Math.Sqrt(s2 / data.Length);
deviation *= k;
double minimum = average - deviation;
double maximum = average + deviation;
return(new Interval(minimum, maximum));
}
private static bool CalculateLinearFastInternal(Portfolio portfolio, bool[] zeros, double[,] sigma, double[] profit, double[] margin, double reliability, double maximumLoss,
double minimumCoefficientValue, double marginThreshold)
{
int count = 0;
Dictionary <int, int> map = new Dictionary <int, int>();
for (int index = 0; index < zeros.Length; ++index)
{
bool status = zeros[index];
if (!status)
{
map[map.Count] = index;
++count;
}
}
if (0 == count)
{
return(true); // nothing to do
}
// create sub-matrix
double[,] _sigma = new double[count, count];
double[] _profit = new double[count];
double[] _margin = new double[count];
for (int row = 0; row < _profit.Length; ++row)
{
int r = map[row];
_profit[row] = profit[r];
_margin[row] = margin[r];
for (int column = 0; column < _profit.Length; ++column)
{
int c = map[column];
_sigma[row, column] = sigma[r, c];
}
}
// calculate factor and check it
double factor = NumericalMethods.Sqrt(_sigma.Maximum());
if (factor <= 0)
{
string st = string.Format("Runtime error: invalid factor = {0}", factor);
throw new InvalidOperationException(st);
}
// normalize data
NumericalMethods.Multiply(_sigma, 1 / factor / factor);
NumericalMethods.Multiply(_profit, 1 / factor);
NumericalMethods.Multiply(_margin, 1 / factor);
MathArgs args = new MathArgs();
args.Add("$profit", _profit);
args.Add("$reliability", reliability);
args.Add("$covariance", _sigma);
args.Add("$loss", maximumLoss / factor);
args.Add("$threshold", marginThreshold / factor);
args.Add("$margin", _margin);
Dictionary <string, object> output = MathematicaKernel.Execute(s_portfolioMargin, args);
double[] coefficients = (double[])output["result"];
// check results
bool result = FastPositiveMinimalThreshold(zeros, minimumCoefficientValue, count, map, coefficients);
if (!result)
{
return(result);
}
// prepare results
for (int index = 0; index < count; ++index)
{
portfolio.Coefficients[map[index]] = coefficients[index];
}
portfolio.Profit = (double)output["profit"] * factor;
portfolio.When = (double)output["when"];
return(result);
}